few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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for free access to Student Response.
Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Thought: This activity asks students to reason how shapes can combine to make other shapes.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

1
options: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Understand ratio concepts and use ratio reasoning to solve problems.
problem_activity: Activity
This activity revisits a context seen previously. Students solved problems like this as early as grade 3 without formulating them in terms of ratios or rates (“If 1 cup of rice serves 3 people, how many people can you serve with 12 cups of rice?”). In this activity, they ultimately find an equation for the proportional relationship.
As students find missing values in the table, they should see that they can always multiply the number of food items by the constant of proportionality. When students see this pattern (MP7) and represent the number of people served by
\(x\)
cups of rice (or
\(s\)
spring rolls) as
\(3x\)
(or
\(\frac{1}{2}s\)
), they are expressing regularity in repeated reasoning (MP8).
Only one row in each table is complete. Based on their experience in the previous lesson, students are more likely to multiply the entries in the left-hand column by 3 (or
\(\frac{1}{2}\)
) than to use scale factors, at least for the first and third rows. If they do, they are more likely to see how to complete the last row in each table.
Some students might use unit rates: If 1 cup of rice can serve 3 people, then
\(x\)
cups of rice can serve
\(3x\)
people. So, students have different ways to generate
\(3x\)
as the expression that represents the number of people served by
\(x\)
cups of rice: completing the table for numerical values and continuing the pattern to the last row; or finding the unit rate and using it in the case of
\(x\)
cups.
Monitor students for different approaches as they are working.
Launch
Tell students that this activity revisits a context they worked on in an earlier lesson.
Student Facing
A recipe says that 2 cups of dry rice will serve 6 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
How many people will 1 cup of rice serve?
How many people will 3 cups of rice serve? 12 cups? 43 cups?
How many people will
\(x\)
cups of rice serve?
| cups of dry rice | number of people |
|------------------|------------------|
|        1         |                  |
|        2         |        6         |
|        3         |                  |
|        12        |                  |
|        43        |                  |
|      \(x\)       |                  |
A recipe says that 6 spring rolls will serve 3 people. Complete the table as you answer the questions. Be prepared to explain your reasoning.
How many people will 1 spring roll serve?
How many people will 10 spring rolls serve? 16 spring rolls? 25 spring rolls?
How many people will
\(n\)
spring rolls serve?
| number of spring rolls | number of people |
|------------------------|------------------|
|           1            |                  |
|           6            |        3         |
|           10           |                  |
|           16           |                  |
|           25           |                  |
|         \(n\)          |                  |
How was completing this table different from the previous table? How was it the same?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
If students have trouble encapsulating the relationship with an expression, encourage them to draw diagrams or to verbalize the relationship in words.
Activity Synthesis
Select students who have used the following approaches in the given order:
Recognize that to move from the first column to the second, you multiply by 3.
Say that 3 is the constant of proportionality.
Recognize that the equation
\(2 \boldcdot  {?} = 6\)
can be used to find the constant of proportionality algebraically.
Say that the 3 can be interpreted as the number of people per 1 cup of rice.
If no student sees that these insights are connected to prior work, explicitly connect them with the lessons of the previous two days. At the end of the discussion, suggest to students that we let
\(y\)
represent the number of people who can be served by
\(x\)
cups of rice. Ask students to write an equation that gives the relationship of
\(x\)
and
\(y\)
. (This builds on work from grade 6, but it may be rusty.) Be sure to write the equation
\(y = 3x\)
where all students can see it and help students interpret its meaning in the context: “To find
\(y\)
, the number of people served, we can multiply the number of cups of rice,
\(x\)
, by 3.”
Representation: Internalize Comprehension.
Use color and annotations to illustrate student thinking. As students describe their approaches, use color and annotations to scribe their thinking on a display.
Supports accessibility for: Visual-spatial processing; Conceptual processing
Conversing: MLR7 Compare and Connect.
As students explain their different approaches to completing the tables, ask “What is similar, what is different?” about their methods. Draw students’ attention to the different ways the constant of proportionality was represented across the different strategies. For instance, when discussing first question, ask “Where do you see the 3 in each approach?” These exchanges strengthen students’ mathematical language use and reasoning based on constant of proportionality.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


correct_option_index: 0